MFC: An open-source high-order multi-component, multi-phase, and multi-scale compressible flow solver

MFC is an open-source tool for solving multi-component, multi-phase, and bubbly compressible flows. It is capable of efficiently solving a wide range of flows, including droplet atomization, shock–bubble interaction, and bubble dynamics. We present the 5- and 6-equation thermodynamically-consistent diffuse-interface models we use to handle such flows, which are coupled to high-order interface-capturing methods, HLL-type Riemann solvers, and TVD time-integration schemes that are capable of simulating unsteady flows with strong shocks. The numerical methods are implemented in a flexible, modular framework that is amenable to future development. The methods we employ are validated via comparisons to experimental results for shock–bubble, shock–droplet, and shock–water-cylinder interaction problems and verified to be free of spurious oscillations for material-interface advection and gas–liquid Riemann problems. For smooth solutions, such as the advection of an isentropic vortex, the methods are verified to be high-order accurate. Illustrative examples involving shock–bubble-vessel-wall and acoustic–bubble-net interactions are used to demonstrate the full capabilities of MFC

A unified Eulerian framework for multimaterial continuum mechanics

A framework for simulating the interactions between multiple different continua is presented. Each constituent material is governed by the same set of equations, differing only in terms of their equations of state and strain dissipation functions. The interfaces between any combination of fluids, solids, and vacuum are handled by a new Riemann Ghost Fluid Method, which is agnostic to the type of material on either side (depending only on the desired boundary conditions). The Godunov-Peshkov-Romenski (GPR) model is used for modelling the continua (having recently been used to solve a range of problems involving Newtonian and non-Newtonian fluids, and elastic and elastoplastic solids), and this study represents a novel approach for handling multimaterial problems under this model. The resulting framework is simple, yet capable of accurately reproducing a wide range of different physical scenarios. It is demonstrated here to accurately reproduce analytical results for known Riemann problems, and to produce expected results in other cases, including some featuring heat conduction across interfaces, and impact-induced deformation and detonation of combustible materials. The framework thus has the potential to streamline development of simulation software for scenarios involving multiple materials and phases of matter, by reducing the number of different systems of equations that require solvers, and cutting down on the amount of theoretical work required to deal with the interfaces between materials.EPSRC Centre for Doctoral Training in Computational Methods for Materials Science under grant EP/L015552/

Eulerian-Lagrangian method for simulation of cloud cavitation

We present a coupled Eulerian-Lagrangian method to simulate cloud cavitation in a compressible liquid. The method is designed to capture the strong, volumetric oscillations of each bubble and the bubble-scattered acoustics. The dynamics of the bubbly mixture is formulated using volume-averaged equations of motion. The continuous phase is discretized on an Eulerian grid and integrated using a high-order, finite-volume weighted essentially non-oscillatory (WENO) scheme, while the gas phase is modeled as spherical, Lagrangian point-bubbles at the sub-grid scale, each of whose radial evolution is tracked by solving the Keller-Miksis equation. The volume of bubbles is mapped onto the Eulerian grid as the void fraction by using a regularization (smearing) kernel. In the most general case, where the bubble distribution is arbitrary, three-dimensional Cartesian grids are used for spatial discretization. In order to reduce the computational cost for problems possessing translational or rotational homogeneities, we spatially average the governing equations along the direction of symmetry and discretize the continuous phase on two-dimensional or axi-symmetric grids, respectively. We specify a regularization kernel that maps the three-dimensional distribution of bubbles onto the field of an averaged two-dimensional or axi-symmetric void fraction. A closure is developed to model the pressure fluctuations at the sub-grid scale as synthetic noise. For the examples considered here, modeling the sub-grid pressure fluctuations as white noise agrees a priori with computed distributions from three-dimensional simulations, and suffices, a posteriori, to accurately reproduce the statistics of the bubble dynamics. The numerical method and its verification are described by considering test cases of the dynamics of a single bubble and cloud cavitaiton induced by ultrasound fields.Comment: 28 pages, 16 figure

A multimaterial Eulerian approach for fluid-solid interaction

This thesis is devoted to understanding and modeling multimaterial interactions, and to develop accordingly a robust scheme taking into account the largest variety of those, with a particular interest in resolving solid/fluid configurations. This very general frame of studies can be tackled with numerous different approaches as several issues arise and need to be addressed before attempting any modelisation of these problems. A first questioning should be the frame of reference to be used for the materials considered. Eulerian shock-capturing schemes have advantages for modeling problems involving complex non-linear wave structures and large deformations. If originally reserved mostly to fluids components, recent work has focused on extending Eulerian schemes to other media such as solid dynamics, as long as the set of equations employed is written under a hyperbolic system of conservation laws. Another matter of interest when dealing with multiple immiscible materials it the necessity to include some means of tracking material boundaries within a numerical scheme. Interface tracking methods based on the use of level set functions are an attractive alternative for problems with sliding interfaces since it allows discontinuous velocity profiles at the material boundaries whilst employing fixed grids. However, its intrinsic lack of variables conservation needs to be circumvented by applying an appropriate fix near the interface, where cells might comprise multiple components. Another requirement is the ability to correctly predict the physical interaction at the interface between the materials. For that purpose, the Riemann problem corresponding to the interfacial conditions needs to be formulated and solved. This implies in turn the need of appropriate Riemann solvers; if they are largely available when the materials are identical (i.e. governed by the same set of equations), a specific Riemann solver will be developed to account for fluid/solid interaction. Eventually, these newly developed methods will be tested on a wide range of different multimaterial problems, involving several materials undergoing large deformations. The materials used, whether modelling fluid/fluid or solid/fluid interactions, will be tested using various initial conditions from both sides of the interface, to demonstrate the robustness of the solver and its flexibility. These testcases will be carried out in 1D, 2D and 3D frames, and compared to exact solutions or other numerical experiments conducted in previous studies.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

A Moving Boundary Flux Stabilization Method for Cartesian Cut-Cell Grids using Directional Operator Splitting

An explicit moving boundary method for the numerical solution of time-dependent hyperbolic conservation laws on grids produced by the intersection of complex geometries with a regular Cartesian grid is presented. As it employs directional operator splitting, implementation of the scheme is rather straightforward. Extending the method for static walls from Klein et al., Phil. Trans. Roy. Soc., A367, no. 1907, 4559-4575 (2009), the scheme calculates fluxes needed for a conservative update of the near-wall cut-cells as linear combinations of standard fluxes from a one-dimensional extended stencil. Here the standard fluxes are those obtained without regard to the small sub-cell problem, and the linear combination weights involve detailed information regarding the cut-cell geometry. This linear combination of standard fluxes stabilizes the updates such that the time-step yielding marginal stability for arbitrarily small cut-cells is of the same order as that for regular cells. Moreover, it renders the approach compatible with a wide range of existing numerical flux-approximation methods. The scheme is extended here to time dependent rigid boundaries by reformulating the linear combination weights of the stabilizing flux stencil to account for the time dependence of cut-cell volume and interface area fractions. The two-dimensional tests discussed include advection in a channel oriented at an oblique angle to the Cartesian computational mesh, cylinders with circular and triangular cross-section passing through a stationary shock wave, a piston moving through an open-ended shock tube, and the flow around an oscillating NACA 0012 aerofoil profile.Comment: 30 pages, 27 figures, 3 table

MFC: An open-source high-order multi-component, multi-phase, and multi-scale compressible flow solver

MFC is an open-source tool for solving multi-component, multi-phase, and bubbly compressible flows. It is capable of efficiently solving a wide range of flows, including droplet atomization, shock–bubble interaction, and bubble dynamics. We present the 5- and 6-equation thermodynamically-consistent diffuse-interface models we use to handle such flows, which are coupled to high-order interface-capturing methods, HLL-type Riemann solvers, and TVD time-integration schemes that are capable of simulating unsteady flows with strong shocks. The numerical methods are implemented in a flexible, modular framework that is amenable to future development. The methods we employ are validated via comparisons to experimental results for shock–bubble, shock–droplet, and shock–water-cylinder interaction problems and verified to be free of spurious oscillations for material-interface advection and gas–liquid Riemann problems. For smooth solutions, such as the advection of an isentropic vortex, the methods are verified to be high-order accurate. Illustrative examples involving shock–bubble-vessel-wall and acoustic–bubble-net interactions are used to demonstrate the full capabilities of MFC